SnowMasaya · February 8, 2018 09:35
diff --git a/file0.py b/file0.py
 import numpy as np
 import pandas as pd
 import pyflux as pf
 from datetime import datetime
 import matplotlib.pyplot as plt
 %matplotlib inline

 data = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/sunspot.year.csv')
 data.index = data['time'].values

 plt.figure(figsize=(15, 5))
 plt.plot(data.index, data['sunspot.year'])
 plt.ylabel('Sunspots')
 plt.title('Yearly Sunspot Data')
diff --git a/file1.py b/file1.py
 model = pf.ARIMA(data=data, ar=4, ma=4, target='sunspot.year', family=pf.Normal())
diff --git a/file10.py b/file10.py
 data = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/MASS/drivers.csv')
 data.index = data['time']

 plt.figure(figsize=(15, 5))
 plt.plot(data.index, data['drivers'])
 plt.ylabel('Driver Deaths')
 plt.title('Deaths of Car Drivers in Great Britain 1969-84')
 plt.plot()
 data_d = data['drivers']
diff --git a/file11.py b/file11.py
 data.loc[(data['time']>=1983.05), 'seat_belt'] = 1;
 data.loc[(data['time']<1983.05), 'seat_belt'] = 0;
 data.loc[(data['time']>=1974.00), 'oil_crisis'] = 1;
 data.loc[(data['time']<1974.00), 'oil_crisis'] = 0;
 plt.figure(figsize=(15, 5))
 plt.plot(data.index, data['drivers'])
 plt.ylabel('Driver Deaths')
 plt.title('Deaths of Car Drivers in Great Britain 1969-84')
 plt.plot()
diff --git a/file12.txt b/file12.txt
 model = pf.ARIMAX(data=data, formula='drivers~1+seat_belt',
                 ar=1, ma=1, family=pf.Normal())
diff --git a/file13.py b/file13.py
 model = pf.ARIMAX(data=data, formula='drivers~1+oil_crisis',
                 ar=1, ma=1, family=pf.Normal())
diff --git a/file14.py b/file14.py
 model = pf.ARIMAX(data=data, formula='drivers~1+seat_belt+oil_crisis',
                 ar=1, ma=1, family=pf.Normal())
diff --git a/file15.txt b/file15.txt
 y_{t} = Z_t\alpha_t+\epsilon_t
diff --git a/file16.txt b/file16.txt
 \alpha_{t} = T_t\alpha_{t-1}+\eta_t
diff --git a/file17.txt b/file17.txt
 \epsilon_{t} \sim N(0, \Sigma^{2}_{\epsilon})
diff --git a/file18.txt b/file18.txt
 \eta_{t} \sim N(0, \Sigma_{\eta})
diff --git a/file19.txt b/file19.txt
 \alpha_{t+1} = \alpha_{t} + K_t(y_t - Z_t\alpha_t)
diff --git a/file2.py b/file2.py
 x = model.fit('MLE')
diff --git a/file20.txt b/file20.txt
 y_{t} = \mu_t+\epsilon_t
diff --git a/file21.txt b/file21.txt
 \mu_{t} = \mu_{t-1}+\eta_t
diff --git a/file22.txt b/file22.txt
 \epsilon_{t} \sim N(0, \sigma^{2}_{\epsilon})
diff --git a/file23.txt b/file23.txt
 \eta_{t} \sim N(0, \sigma^{2}_{\eta})
diff --git a/file24.py b/file24.py
 nile = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/Nile.csv')
 nile.index = pd.to_datetime(nile['time'].values,format='%Y')
 plt.figure(figsize=(15,5))
 plt.plot(nile.index,nile['Nile'])
 plt.ylabel('Discharge Volume')
 plt.title('Nile River Discharge');
 plt.show()
diff --git a/file25.py b/file25.py
 model = pf.LocalLevel(data=nile, target='Nile', family=pf.Normal())
 x = model.fit()
 x.summary()
diff --git a/file26.txt b/file26.txt
 LLEV                                                                                                      
 ======================================================= ==================================================
 Dependent Variable: Nile                                Method: MLE                                       
 Start Date: 1871-01-01 00:00:00                         Log Likelihood: -641.5238                         
 End Date: 1970-01-01 00:00:00                           AIC: 1287.0476                                    
 Number of observations: 100                             BIC: 1292.258                                     
 ==========================================================================================================
 Latent Variable                          Estimate   Std Error  z        P>|z|    95% C.I.                 
 ======================================== ========== ========== ======== ======== =========================
 Sigma^2 irregular                        15098.5410                                                       
 Sigma^2 level                            1469.13678                                                       
 ==========================================================================================================
diff --git a/file27.py b/file27.py
 model.plot_fit(figsize=(15,10))
diff --git a/file28.txt b/file28.txt
 y_{t} = \sum^{P}_{i=1}\phi_{i,t}y_{t-i}+\epsilon_t
diff --git a/file29.txt b/file29.txt
 \phi_{i,t} = \phi_{i,t-1}+\eta_t
diff --git a/file3.py b/file3.py
 x.summary()
diff --git a/file30.txt b/file30.txt
 \epsilon_{t} \sim N(0, \sigma^{2}_{\epsilon})
diff --git a/file31.txt b/file31.txt
 \eta_{t} \sim N(0, \sigma^{2}_{\eta})
diff --git a/file32.py b/file32.py
 data = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/sunspot.year.csv')
 model= pf.DAR(data=data, ar=9, integ=0, target='sunspot.year')
 x = model.fit('MLE')
 x.summary()
diff --git a/file33.txt b/file33.txt
 y_{t+1} = \phi y_t + \theta(y_t - \mu_t)
diff --git a/file34.txt b/file34.txt
 (y_t - \mu_t)
diff --git a/file35.txt b/file35.txt
 p(y_t) = \frac{1}{\sqrt{2\pi\sigma^2}}\exp(-\frac{(y_t-\mu)^2}{2\sigma^2})
diff --git a/file36.txt b/file36.txt
 \log p(y_t) = \frac{1}{2}\log(2\pi\sigma^2)-\frac{1}{2}\frac{(y_t-\mu)^2}{\sigma^2}
diff --git a/file37.txt b/file37.txt
 \nabla_{\mu_t}\log p(y_t) = \frac{(y_t-\mu)^2}{\sigma^2}
diff --git a/file38.txt b/file38.txt
 \nabla^{2}_{\mu_t}\log p(y_t) = \frac{1}{\sigma^2}
diff --git a/file39.txt b/file39.txt
 \frac{\nabla_{\mu_t}\log p(y_t)}{-\nabla^{2}_{\mu_t}\log p(y_t)} = (y_t-\mu)
diff --git a/file4.txt b/file4.txt
 Normal ARIMA(4,0,4)                                                                                       
 ======================================================= ==================================================
 Dependent Variable: sunspot.year                        Method: MLE                                       
 Start Date: 1704                                        Log Likelihood: -1191.0131                        
 End Date: 1988                                          AIC: 2402.0263                                    
 Number of observations: 285                             BIC: 2438.5512                                    
 ==========================================================================================================
 Latent Variable                          Estimate   Std Error  z        P>|z|    95% C.I.                 
 ======================================== ========== ========== ======== ======== =========================
 Constant                                 11.5047    3.7053     3.1049   0.0019   (4.2422 | 18.7672)       
 AR(1)                                    1.4764     0.0738     20.0147  0.0      (1.3318 | 1.621)         
 AR(2)                                    -0.2544    0.2076     -1.2257  0.2203   (-0.6613 | 0.1524)       
 AR(3)                                    -0.9033    0.1831     -4.932   0.0      (-1.2622 | -0.5443)      
 AR(4)                                    0.452      0.0761     5.9379   0.0      (0.3028 | 0.6013)        
 MA(1)                                    -0.2985    0.0727     -4.1047  0.0      (-0.441 | -0.156)        
 MA(2)                                    -0.497     0.1008     -4.9307  0.0      (-0.6946 | -0.2995)      
 MA(3)                                    0.1824     0.0988     1.8468   0.0648   (-0.0112 | 0.376)        
 MA(4)                                    0.329      0.0837     3.9315   0.0001   (0.165 | 0.4931)         
 Normal Scale                             15.8645                                                          
 ==========================================================================================================
diff --git a/file40.txt b/file40.txt
 \lambda_t = \exp(\theta_t)
diff --git a/file41.txt b/file41.txt
 p(y_t) = \frac{\exp(\theta_t)^{y_t}\exp^{-\exp(\theta_t)}}{y_t!}
diff --git a/file42.txt b/file42.txt
 \log p(y_t) = y_t\theta_t-\exp(\theta_t)-\log(y_t!)
diff --git a/file43.txt b/file43.txt
 \nabla_{\theta_t}\log p(y_t) = y_t-\exp(\theta_t)
diff --git a/file44.txt b/file44.txt
 \nabla^2_{\theta_t}\log p(y_t) = -\exp(\theta_t)
diff --git a/file45.txt b/file45.txt
 \frac{\nabla_{\mu_t}\log p(y_t)}{-\nabla^{2}_{\mu_t}\log p(y_t)} = \frac{1}{\exp(\theta_t)}(y_t-\exp(\theta_t))
diff --git a/file46.py b/file46.py
 leicester = pd.read_csv('http://www.pyflux.com/notebooks/leicester_goals_scored.csv')
 leicester.columns= ["Time","Goals","Season2"]
 plt.figure(figsize=(15,5))
 plt.plot(leicester["Goals"])
 plt.ylabel('Goals Scored')
 plt.title('Leicester Goals Since Joining EPL');
 plt.show()
diff --git a/file47.py b/file47.py
 model = pf.LocalLevel(data=leicester, target='Goals', family=pf.Poisson())
diff --git a/file48.py b/file48.py
 x = model.fit(iterations=5000)
 x.summary()
diff --git a/file49.txt b/file49.txt
 10% done : ELBO is -251.57569112887904, p(y,z) is -166.3745900900033, q(z) is 85.20110103887575
 20% done : ELBO is -251.0404488657637, p(y,z) is -163.08148512110355, q(z) is 87.95896374466014
 30% done : ELBO is -248.3826857773143, p(y,z) is -160.95781417531765, q(z) is 87.42487160199666
 40% done : ELBO is -243.78188227888018, p(y,z) is -158.15537328287218, q(z) is 85.62650899600798
 50% done : ELBO is -240.84398713641178, p(y,z) is -156.96138472006595, q(z) is 83.88260241634582
 60% done : ELBO is -238.7879147438848, p(y,z) is -156.14707335243622, q(z) is 82.6408413914486
 70% done : ELBO is -237.27773593445806, p(y,z) is -155.37226587768643, q(z) is 81.90547005677165
 80% done : ELBO is -234.66469485120308, p(y,z) is -153.9445088318954, q(z) is 80.72018601930766
 90% done : ELBO is -234.21050603276024, p(y,z) is -153.86353460095933, q(z) is 80.34697143180091
 100% done : ELBO is -232.41596530920148, p(y,z) is -153.02493554086158, q(z) is 79.3910297683399

 Final model ELBO is -232.6451770092436
 Poisson Local Level Model                                                                                 
 ======================================================= ==================================================
 Dependent Variable: Goals                               Method: BBVI                                      
 Start Date: 0                                           Unnormalized Log Posterior: -153.3266             
 End Date: 74                                            AIC: 308.65314788761225                           
 Number of observations: 75                              BIC: 310.97063600114853                           
 ==========================================================================================================
 Latent Variable                          Median             Mean               95% Credibility Interval 
 ======================================== ================== ================== =========================
 Sigma^2 level                            0.0404             0.0404             (0.0353 | 0.0462)        
 ==========================================================================================================
diff --git a/file5.py b/file5.py
 model.plot_z(figsize=(15, 5))
diff --git a/file50.py b/file50.py
 model.plot_fit(figsize=(15,10))
diff --git a/file6.py b/file6.py
 model.plot_fit(figsize=(15, 10))
diff --git a/file7.py b/file7.py
 model.plot_predict_is(h=50, figsize=(15, 10))
diff --git a/file8.py b/file8.py
 model.plot_predict(h=20, past_values=20, figsize=(15,5))
diff --git a/file9.txt b/file9.txt
    Unnamed: 0  time            drivers seat_belt oil_crisis
 time                    
 1969.000000 1   1969.000000 1687    0.0   0.0
 1969.083333 2   1969.083333 1508    0.0   0.0
 1969.166667 3   1969.166667 1507    0.0   0.0
	import numpy as np
	import pandas as pd
	import pyflux as pf
	from datetime import datetime
	import matplotlib.pyplot as plt
	%matplotlib inline

	data = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/sunspot.year.csv')
	data.index = data['time'].values

	plt.figure(figsize=(15, 5))
	plt.plot(data.index, data['sunspot.year'])
	plt.ylabel('Sunspots')
	plt.title('Yearly Sunspot Data')
	data = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/MASS/drivers.csv')
	data.index = data['time']

	plt.figure(figsize=(15, 5))
	plt.plot(data.index, data['drivers'])
	plt.ylabel('Driver Deaths')
	plt.title('Deaths of Car Drivers in Great Britain 1969-84')
	plt.plot()
	data_d = data['drivers']
	data.loc[(data['time']>=1983.05), 'seat_belt'] = 1;
	data.loc[(data['time']<1983.05), 'seat_belt'] = 0;
	data.loc[(data['time']>=1974.00), 'oil_crisis'] = 1;
	data.loc[(data['time']<1974.00), 'oil_crisis'] = 0;
	plt.figure(figsize=(15, 5))
	plt.plot(data.index, data['drivers'])
	plt.ylabel('Driver Deaths')
	plt.title('Deaths of Car Drivers in Great Britain 1969-84')
	plt.plot()
	model = pf.ARIMAX(data=data, formula='drivers~1+seat_belt',
	ar=1, ma=1, family=pf.Normal())
	nile = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/Nile.csv')
	nile.index = pd.to_datetime(nile['time'].values,format='%Y')
	plt.figure(figsize=(15,5))
	plt.plot(nile.index,nile['Nile'])
	plt.ylabel('Discharge Volume')
	plt.title('Nile River Discharge');
	plt.show()
	model = pf.LocalLevel(data=nile, target='Nile', family=pf.Normal())
	x = model.fit()
	x.summary()
	LLEV
	======================================================= ==================================================
	Dependent Variable: Nile Method: MLE
	Start Date: 1871-01-01 00:00:00 Log Likelihood: -641.5238
	End Date: 1970-01-01 00:00:00 AIC: 1287.0476
	Number of observations: 100 BIC: 1292.258
	==========================================================================================================
	Latent Variable Estimate Std Error z P>\|z\| 95% C.I.
	======================================== ========== ========== ======== ======== =========================
	Sigma^2 irregular 15098.5410
	Sigma^2 level 1469.13678
	==========================================================================================================
	data = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/sunspot.year.csv')
	model= pf.DAR(data=data, ar=9, integ=0, target='sunspot.year')
	x = model.fit('MLE')
	x.summary()
	Normal ARIMA(4,0,4)
	======================================================= ==================================================
	Dependent Variable: sunspot.year Method: MLE
	Start Date: 1704 Log Likelihood: -1191.0131
	End Date: 1988 AIC: 2402.0263
	Number of observations: 285 BIC: 2438.5512
	==========================================================================================================
	Latent Variable Estimate Std Error z P>\|z\| 95% C.I.
	======================================== ========== ========== ======== ======== =========================
	Constant 11.5047 3.7053 3.1049 0.0019 (4.2422 \| 18.7672)
	AR(1) 1.4764 0.0738 20.0147 0.0 (1.3318 \| 1.621)
	AR(2) -0.2544 0.2076 -1.2257 0.2203 (-0.6613 \| 0.1524)
	AR(3) -0.9033 0.1831 -4.932 0.0 (-1.2622 \| -0.5443)
	AR(4) 0.452 0.0761 5.9379 0.0 (0.3028 \| 0.6013)
	MA(1) -0.2985 0.0727 -4.1047 0.0 (-0.441 \| -0.156)
	MA(2) -0.497 0.1008 -4.9307 0.0 (-0.6946 \| -0.2995)
	MA(3) 0.1824 0.0988 1.8468 0.0648 (-0.0112 \| 0.376)
	MA(4) 0.329 0.0837 3.9315 0.0001 (0.165 \| 0.4931)
	Normal Scale 15.8645
	==========================================================================================================
	leicester = pd.read_csv('http://www.pyflux.com/notebooks/leicester_goals_scored.csv')
	leicester.columns= ["Time","Goals","Season2"]
	plt.figure(figsize=(15,5))
	plt.plot(leicester["Goals"])
	plt.ylabel('Goals Scored')
	plt.title('Leicester Goals Since Joining EPL');
	plt.show()